We now define sub-Weibull random variables, as is done in [1]}.
We call a random variable \(X_j\)  sub-Weibull with tail parameter \(\theta \)  if there exists \(\theta ,a,b > 0\) 
such that
\( \forall x > 0: \operatornamewithlimits{\mathbb {P}}\left( \vert X_j \vert \geqslant x \right) \leqslant a \exp \left( -b x^{1/\theta } \right). \) 
